Center of mass
Have you ever played a game at a carnival, trying to win a stuffed animal or other prize? It might look easy—until you try it. Why are those "simple" games at the fairs, carnivals and Mardi Gras festivals so hard? Is it really lack of skill or coordination or do those midway vendors use some basic laws of science to help them set up the games in their favor? In this science activity you'll investigate how physics can help you win—or lose—at the classic game of trying to knock over a pyramid of milk bottles using a ball.
Why can it be nearly impossible to knock down pins or hit the right target to win that giant stuffed animal at the carnival or fair—especially when it looks so easy? To answer this, in this activity we'll look at the classic carnival game sometimes called "One Ball," in which milk bottles are stacked in a pyramid and you get one throw with a ball to try to knock them all over. To beat this game it's useful to think about how redistributing an object's mass can affect how well it balances. For example, it might be easy to stand on a balance beam while holding a heavy backpack hanging down in front of you, but it's much more challenging when that backpack is on your back.
How an object's mass is distributed can affect its center of mass, which is the average location of most of an object's mass. This basically means that the center of mass will be in the object's center if the mass is evenly distributed on top and bottom (as it usually is with a ball). And it will shift to the object's heavier side if the mass isn't uniformly distributed. So, for a pyramid, the center of mass will be much lower than it's physical center because so much more of the mass is located in the lower half.
- A very large room or an outside area (You will need plenty of space so you can throw a ball without hitting anyone or anything.)
- A small, stable table
- Masking tape, a stick, a rock or a similar object to mark off a throwing distance
- Tennis ball or baseball
- Three plastic bottles filled with water, all the same shape and size (Make sure that you can stably stack the bottles in a pyramid shape. Most 16.9–fluid ounce drinking-water bottles should work well for this.)
- Food coloring (optional)
- Fill each of the bottles with water. The same amount of water should be in each bottle.
- If you want, you can remove the labels from your bottles and add some food coloring (three drops) to each bottle to give your carnival game some color. If you add food coloring to the bottles, make sure you do your testing where it will not be a problem if a bottle spills some dyed water! (If you use dyed water, it's recommended you do this activity outdoors.)
- Take your materials to the very large room or area outside where you can set up your mini carnival game.
- Put the small table at a set distance from your "throw line." You might try about eight feet away from the table. Mark the throw line using a piece of masking tape, a rock, a stick or a similar object.
- Make sure the water bottle lids are on tight. Stack the three bottles into a stable pyramid shape on the table, with two bottles on the bottom and one on top that is centered between them and resting on their lids. How stable is your pyramid?
- From your throw line, throw the tennis ball (or baseball) at the bottle pyramid. Did you hit any bottles? If so, which bottle was hit? How many bottles were knocked over?
- Arrange the pyramid as it was before on the table.
- Repeat this process until you have hit the pyramid at least 10 times with the ball. Try to throw the ball the same way each time, and try to hit each bottle a few times. How many bottles usually get knocked over? Does it seem to depend on which bottle you hit with the ball? If so, which bottle(s) do you need to hit to knock over the most bottles?
- Now take the top bottle from the pyramid and empty the water out of it. Stack the bottles into a stable pyramid shape on the table with the empty bottle on the top. How stable does this pyramid seem?
- As you did before, throw the ball from the throw line at the pyramid at least 10 times, rearranging the pyramid on the table after each throw. Again try to throw the ball the same way each time, and try to hit each bottle a few times. How many bottles usually get knocked over now? Does hitting a certain bottle (or bottles) tend to knock over the most bottles?
- Take one of the bottom bottles from the pyramid and empty the water out of it. Stack the bottles into a stable pyramid shape on the table with the two empty bottles on the bottom and the water-filled bottle on the top. How stable does this pyramid seem?
- As you did before, throw the ball from the throw line at the pyramid at least 10 times, rearranging the pyramid on the table after each throw. Again try to throw the ball the same way each time, and try to hit each bottle a few times. How many bottles usually get knocked over with this pyramid arrangement? Does hitting a certain bottle (or bottles) tend to knock over the most bottles?
- Overall, which pyramid arrangement led to the highest number of throws where all three bottles were knocked over? In other words, which arrangement was most successful? Which was least successful? Which bottle(s) should be hit to cause the largest number of bottles to fall down?
- Extra: You could repeat this activity but this time you could quantify your results. That is, when testing each pyramid arrangement, write down which bottle is hit each time and how many bottles are knocked over. If you quantify your results, just how much more "successful" is one pyramid arrangement compared with another? How much better is it to hit one bottle compared with another?
- Extra: Try moving the throw line closer to the pyramid or farther away from it. How does your throwing distance from the pyramid change how successful you are at knocking it over?
- Extra: Instead of bottles you could use wooden blocks and arrange them in different configurations, such as stacking all three on top of one another. Using wooden blocks, which configuration is easiest to knock over? Which is hardest?
Observations and results
When the pyramid was arranged with two empty bottles on the bottom (and a filled bottle on top), did it fall over the easiest? Was hitting the bottom bottles typically the best approach?
A lot of people may initially think that the center of mass of the first bottle pyramid you made is in the middle of the structure (where the upper bottle rests on the lower ones). But in this configuration, with all of the bottles filled equally, it's actually closer to the middle of the two bottom bottles—because there are two bottles on the bottom, there is more mass on the bottom of the pyramid than the top. So the center of mass is closer to the pyramid's bottom. In the second pyramid arrangement the center of mass became even lower because more mass was in the bottom part of the pyramid compared with the top. In the third pyramid arrangement the center of mass became much higher—somewhere within the top bottle.
You should have found that the third pyramid, with its higher center of mass, was the easiest one to knock over and most unstable, likely having all three bottles fall over when the ball touched any of them. On the other hand, the second pyramid, with its lower center of mass, was likely the hardest to knock over completely. In general, hitting the lower area between the bottom bottles (below the center of mass of the pyramid) should have been the most successful approach for knocking down the entire pyramid. Except for the third pyramid, hitting the top bottle likely only knocked the top bottle off of the pyramid, leaving the two others still standing.
More to explore
The Scientific Method & Carnival Games, from Portage, Inc.
Center of Mass, from High School Online Collaborative Writing
Fun, Science Activities for You and Your Family, from Science Buddies
Knock Your Blocks Off: The Mechanics of Carnival Games, from Science Buddies
This activity brought to you in partnership with Science Buddies